If you didn't notice the shift between third-, second-, and first-person narration, well, you didn't read the book.
The third-person narrator likes to butt into your reading to guide you through the book as a whole, but he also addresses you in the second person, making you the main character of the story. And in case that wasn't confusing enough, all the fictional novels you begin to read are narrated in first-person limited.
Why would Calvino go so crazy with narration? We're guessing it's because this book is an experiment trying to find new ways to tap the potential of novels. Check out, um, any other section of the book for more on this. But he also might be trying to convey his overall point about how one should approach the reading process.
See, the book itself (speaking in third-person omniscient) wants to walk you, the Reader, through an educational journey. But at the same time, it doesn't want you to excuse yourself from its message by saying "well, it's not about me." Instead, it forces you to take on the role of an average or normal reader. This way, the book can tell you things about "yourself" without giving you the option of saying it's wrong, since the book can always pull back at this moment and say "no, not you; the character you're playing."